Problem: If $x \barwedge y = 3x-y$ and $x \dagger y = x^{2}-4y^{2}$, find $-4 \dagger (2 \barwedge 4)$.
Answer: First, find $2 \barwedge 4$ $ 2 \barwedge 4 = (3)(2)-4$ $ \hphantom{2 \barwedge 4} = 2$ Now, find $-4 \dagger 2$ $ -4 \dagger 2 = (-4)^{2}-4(2^{2})$ $ \hphantom{-4 \dagger 2} = 0$.